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A machine learning approach to portfolio pricing and risk management for high‐dimensional problems

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  • Lucio Fernandez‐Arjona
  • Damir Filipović

Abstract

We present a general framework for portfolio risk management in discrete time, based on a replicating martingale. This martingale is learned from a finite sample in a supervised setting. Our method learns the features necessary for an effective low‐dimensional representation, overcoming the curse of dimensionality common to function approximation in high‐dimensional spaces, and applies for a wide range of model distributions. We show numerical results based on polynomial and neural network bases applied to high‐dimensional Gaussian models. In these examples, both bases offer superior results to naive Monte Carlo methods and regress‐now least‐squares Monte Carlo (LSMC).

Suggested Citation

  • Lucio Fernandez‐Arjona & Damir Filipović, 2022. "A machine learning approach to portfolio pricing and risk management for high‐dimensional problems," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 982-1019, October.
    • Handle: RePEc:bla:mathfi:v:32:y:2022:i:4:p:982-1019
    DOI: 10.1111/mafi.12358
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Michael Ludkovski & James Risk, 2017. "Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement," Papers 1710.05204, arXiv.org, revised May 2018.
    3. Kan, Raymond, 2008. "From moments of sum to moments of product," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 542-554, March.
    4. Dilip B. Madan & Frank Milne, 1994. "Contingent Claims Valued And Hedged By Pricing And Investing In A Basis," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 223-245, July.
    5. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2015. "Risk Estimation via Regression," Operations Research, INFORMS, vol. 63(5), pages 1077-1097, October.
    6. Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
    7. Lotfi Boudabsa & Damir Filipovic, 2019. "Machine learning with kernels for portfolio valuation and risk management," Papers 1906.03726, arXiv.org, revised May 2021.
    8. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    9. L. Jeff Hong & Sandeep Juneja & Guangwu Liu, 2017. "Kernel Smoothing for Nested Estimation with Application to Portfolio Risk Measurement," Operations Research, INFORMS, vol. 65(3), pages 657-673, June.
    10. Sébastien Bossu & Peter Carr & Andrew Papanicolaou, 2021. "A functional analysis approach to the static replication of European options," Quantitative Finance, Taylor & Francis Journals, vol. 21(4), pages 637-655, April.
    11. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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